If a, b, c are three distinct numbers in an a | vedclass

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(A) Since $a, b, c$ are in an arithmetic progression,we have $a + c = 2b$ or $c - b = b - a$. Let $d = b - a = c - b$. Given that $b - a, c - b, a$ ar

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$1 : 2 : 3$

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(A) Since $a, b, c$ are in an arithmetic progression,we have $a + c = 2b$ or $c - b = b - a$. Let $d = b - a = c - b$. Given that $b - a, c - b, a$ are in a geometric progression,we have $(c - b)^2 = (b - a)a$. Substituting $d$ into the equation,we get $d^2 = da$. Since the numbers are distinct,$d 
eq 0$,so $d = a$. Now,$b - a = a \implies b = 2a$. Also,$c - b = a \implies c = b + a = 2a + a = 3a$. Therefore,$a : b : c = a : 2a : 3a = 1 : 2 : 3$.

If $a, b, c$ are three distinct numbers in an arithmetic progression,and $b - a, c - b, a$ are in a geometric progression,then $a : b : c = .....$

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